Dear Edwin Eugene,
As I promised in my Essay page, I have read your beautiful Essay. Here are my comments/questions.
1) As I told in my Essay page, I worked and still work on gravito-magnetism. Thus, I have a personal interest in your Essay.
2) You extend General Relativity by adding your C field. This theory reproduces GR equations, but it represents a Yang-Mills gauge theory of mass. I think that similar results could be, in principle, re-obtained in some extended theories of gravity like scalar-tensor gravity and f(R) theory. You could be interested to extend your non-linear approach in those cases too.
3) Recently, Fromholz, Poisson and Will reformulated the MTW's statement that "any physical theory originally written in a special coordinates system can be recast in geometric, coordinate free language" as "The principle of general covariance, upon which general relativity is built, implies that coordinates are simply labels of spacetime events that can be assigned completely arbitrarily (subject to some conditions of smoothness and differentiability). The only quantities that have physical meaning - the measurables - are those that are invariant under coordinate transformations. One such invariant is the number of ticks on an atomic clock giving the proper time between two events", see http://arxiv.org/abs/1308.0394.
4) I agree with your statement that all energy gravitates, but the problem is that, based on Einstein Equivalence Principle, the gravitational energy cannot be localized! This is in perfect agreement with Yau's statement and is also connected to Kauffmann's work recently noted by FQXi.
5) I think that solar system tests of gravity should put some constrains to the C-filed. In general, deviations from standard GR must be weak for a theory to be viable. Thus, I suggest you to extend your work in this direction too.
6) Concerning the linearization process, do you think that the C-field should enable more gravity-waves polarizations than the two standard polarizations of GR?
In any case, I found your Essay a bite provocative and also interesting. As I appreciate people who "think outside the box", I will give you a high rate.
Cheers,
Ch.